Internal combustion engine cylinder air-fuel ratio imbalance detection and controls

ABSTRACT

A system for detecting and controlling air-fuel ratio imbalance conditions between cylinders of an internal combustion engine having a plurality of cylinders is disclosed.

CROSS-REFERENCE TO RELATED APPLICATION

The present application is a continuation of International PatentApplication No. PCT/US17/64010 filed on Nov. 30, 2017, which claims thebenefit of the filing date of U.S. Provisional App. Ser. No. 62/428,656filed on Dec. 1, 2016, which are incorporated herein by reference.

BACKGROUND

Internal combustion engines typically operate by introducing a mixtureof air and fuel into a cylinder of an engine. A piston then compressesthis mixture, and, depending on whether the engine is a compressionignition or spark ignition engine, the mixture combusts or is ignited inthe cylinder. The ratio of air to fuel, or air-fuel ratio (AFR), in eachcylinder during combustion is critical for engine performance andemissions control. For example, three-way catalysts deteriorate severelyif the cylinder-to-cylinder AFR imbalance is present. Furthermore,having the same AFR between each cylinder of a plurality of cylinders isimportant in AFR control. Variations in AFR between cylinders, orcylinder imbalance, can result in higher emissions, higher fuelconsumption, knock, and misfire, among other issues. Also, regulatorybodies are now requiring the detection of AFR imbalance as part ofon-board diagnostic requirements. Therefore, further improvements in AFRimbalance diagnostics and/or controls of internal combustion engines areneeded.

SUMMARY

One embodiment is a unique system for diagnosing and/or controlling AFRvariation/imbalance between cylinders of an internal combustion enginehaving a plurality of cylinders. Other embodiments include uniquemethods, systems, and apparatus to determine an AFR imbalance among theplurality of cylinders. In a further embodiment, the AFR imbalance isdetermined based on a time domain frequency analysis, recursive nonparametric spectral analysis, and/or a parametric spectral analysisusing real time model identification.

This summary is provided to introduce a selection of concepts that arefurther described below in the illustrative embodiments. This summary isnot intended to identify key or essential features of the claimedsubject matter, nor is it intended to be used as an aid in limiting thescope of the claimed subject matter. Further embodiments, forms,objects, features, advantages, aspects, and benefits shall becomeapparent from the following description and drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic depiction of one embodiment of a system having anengine with an exhaust system, an intake system, an EGR system, a fuelsystem, a turbocharger system and a control apparatus.

FIG. 2 is a schematic depiction of one embodiment of the controlapparatus of the system of FIG. 1.

FIGS. 3A and 3B show a balanced condition and an unbalanced condition,respectively, between the sensed output lambda and the feedback controlinput lambda.

FIG. 4A shows the input/output references for feedback control inputlambda and sensed output lambda and FIG. 4B shows a sensor measurementwith dithering and imbalance.

FIG. 5 is a chart of frequency versus voltage for an example operatingcondition of a sensor that senses the output lambda.

FIG. 6 is a graphical illustration of parametric spectral analysis inthe time domain and in the frequency domain.

DESCRIPTION OF ILLUSTRATIVE EMBODIMENTS

For the purposes of promoting an understanding of the principles of theinvention, reference will now be made to the embodiments illustrated inthe drawings and specific language will be used to describe the same. Itwill nevertheless be understood that no limitation of the scope of theinvention is thereby intended, any alterations and further modificationsin the illustrated embodiments, and any further applications of theprinciples of the invention as illustrated therein as would normallyoccur to one skilled in the art to which the invention relates arecontemplated herein.

Referencing FIG. 1, a system 100 is depicted having an engine 102 and anexhaust system 104. The engine 102 is an internal combustion engine ofany type, and can include a stoichiometric engine, such as a natural gasengine, and/or a gasoline engine. In certain embodiments, the engine 102is a combustion engine such as a natural gas engine, althoughembodiments with a gasoline engine, a diesel cycle engine, andcombinations of these such as dual fuel engines are also contemplated.In certain embodiments, the engine 102 may be any engine type producingemissions that includes an exhaust gas recirculation (EGR) system 106,for example to reduce NO_(x) emissions from the engine 102. The engine102 includes a number of cylinders 108. The number of cylinders may beany number suitable for an engine, and the arrangement may be anysuitable arrangement, such as an in-line or V-shaped arrangement. Thesystem 100 includes an in-line six cylinder arrangement for illustrationpurposes only. The example engine 102 may further include an ignitionsource such as a spark plug (not shown) in certain embodiments.

In certain embodiments, the engine 102 is provided as a stoichiometricspark-ignition internal combustion engine, configured to developmechanical power from internal combustion of a stoichiometric mixture offuel and induction gas. As used herein, the phrase “induction gas”includes a charge flow, and may include fresh air, recirculated exhaustgases, or the like, or any combination thereof. The intake 110 includesan intake manifold 112 that receives charge flow from an intake passage114 and distributes the induction gas to combustion chambers ofcylinders 108 of the engine 102. Accordingly, an inlet of the intakemanifold 112 is disposed downstream of an outlet of the intake passage114, and an outlet of the intake manifold 112 is disposed upstream of aninlet of each of the combustion chambers in engine 102. An exhaustmanifold 116 collects exhaust gases from combustion chambers ofcylinders 108 of the engine 102 and conveys the exhaust gases to EGRpassage 118 of EGR system 106 via exhaust passage 120. Accordingly, theinlet of the exhaust manifold 116 is disposed downstream of an outlet ofeach of the combustion chambers of the cylinders 108 in engine 102, andupstream of inlets to the respective EGR passage 118 and exhaust passage120.

Injectors 122 may also be arranged within the engine 102 to deliver fueldirectly or indirectly into the combustion chambers of cylinders 108from a fuel system 130. In another embodiment, fuel is injected into theintake system upstream of the intake manifold 112, such as at the inletof a compressor in the intake 110 or any other suitable location alongintake passage 114. The fuel system 130 is structured to deliver fuel tothe engine 102 in response to a fueling command that provides one ormore of a fuel amount, timing, pressure and duration of fuel injectionto each of the cylinders 108. The fuel system 130 includes a fuel source132, such as a tank or pressurized supply of natural gas. In oneembodiment, the fuel system 130 can be configured to deliver natural gasfuel to the engine 102 from fuel source 132. In another embodiment, thefuel system 130 can be configured to deliver another type of fuel, inaddition to or in lieu of natural gas, to the engine 102. Examples ofsuch additional fuels include gasoline, diesel, ethanol, and the like.In one embodiment, the fuel system 130 may include one or more injectorsconfigured to inject fuel into the engine 102 so that it may becombusted within a combustion chamber. Example injectors include directinjectors, port injectors, and/or fuel valves that inject into intakepassage 114.

In the EGR system 106 of FIG. 1, the EGR flow is created by exhaust gasthat recirculates in EGR passage 118 and combines with fresh air flow inintake passage 114 at a position upstream of intake manifold 112. Intakemanifold 112 provides a charge flow including the intake flow combinedwith the flow to each cylinder 108. Intake passage 114 can includes anintake throttle (not shown) to regulate the charge flow to cylinders108. Intake passage 114 may also include a charge air cooler (not shown)to cool the charge flow provided to intake manifold 112. Intake passage114 can also receive a compressed fresh air flow from a compressor 126of a turbocharger 124. Intake passage 114 can also include a mixer tomix air, gaseous fuel, and EGR for delivery into the intake manifold.Turbocharger 124 also includes a turbine 128 in exhaust passage 120.Turbine 128 is operable via the exhaust gases to drive compressor 126via a rod, shaft or the like. Turbine 128 can be a fixed geometryturbine, a variable geometry turbine with an adjustable inlet, orinclude a wastegate to bypass exhaust flow. It will be appreciated,however, that the turbocharger may be provided in any other suitablemanner (e.g., as a multi-stage turbocharger, or the like), and may beprovided with or without a wastegate and/or bypass. Other embodimentscontemplate an exhaust throttle (not shown) in the exhaust system 104.

The EGR system 106 in the illustrated embodiment is a high pressure EGRsystem connected downstream of compressor 126 and upstream of turbine128. Other embodiments contemplated low pressure EGR systems connectedupstream of compressor 126 and downstream of turbine 128, combined lowpressure and high pressure EGR systems, and dedicated EGR systems, forexample. The example EGR system 106 includes an EGR cooler 134 in theEGR passage 118. In other embodiments, EGR passage 118 can include abypass with a valve that selectively allows EGR flow to bypass the EGRcooler 134. The presence of an EGR cooler 134 and/or an EGR coolerbypass is optional and non-limiting. In certain embodiments, the system100 does not include a compressor or any other type of boost pressuregenerating device in the intake 110.

The exhaust system 104 can further include an aftertreatment system 136in exhaust passage 120 downstream of turbine 128 that is configured totreat emissions in the exhaust gas. Aftertreatment system 136 caninclude any aftertreatment components known in the art. Exampleaftertreatment components treat carbon monoxide (CO), unburnedhydrocarbons (HC), nitrogen oxides (NO_(x)), volatile organic compounds(VOC), and/or particulate matter (PM). Aftertreatment system 138 caninclude a catalyst such as a three-way catalyst, a particulate filter,or any suitable emissions reduction or treating component.

In certain embodiments, the system 100 includes a controller 140structured to perform certain operations to control operations of engine102 and associated fuel system 130. In certain embodiments, thecontroller 140 forms a portion of a processing subsystem including oneor more computing devices having memory, processing, and communicationhardware. The controller 140 may be a single device or a distributeddevice, and the functions of the controller 140 may be performed byhardware or by instructions encoded on computer readable medium. Thecontroller 140 may be included within, partially included within, orcompletely separated from an engine controller (not shown). Thecontroller 140 is in communication with any sensor or actuatorthroughout the system 100, including through direct communication,communication over a datalink, and/or through communication with othercontrollers or portions of the processing subsystem that provide sensorand/or actuator information to the controller 140.

In certain embodiments, the controller 140 is described as functionallyexecuting certain operations. The descriptions herein including thecontroller operations emphasizes the structural independence of thecontroller, and illustrates one grouping of operations andresponsibilities of the controller. Other groupings that execute similaroverall operations are understood within the scope of the presentapplication. Aspects of the controller may be implemented in hardwareand/or by a computer executing instructions stored in non-transientmemory on one or more computer readable media, and the controller may bedistributed across various hardware or computer based components.

Example and non-limiting controller implementation elements includesensors providing any value determined herein, sensors providing anyvalue that is a precursor to a value determined herein, datalink and/ornetwork hardware including communication chips, oscillating crystals,communication links, cables, twisted pair wiring, coaxial wiring,shielded wiring, transmitters, receivers, and/or transceivers, logiccircuits, hard-wired logic circuits, reconfigurable logic circuits in aparticular non-transient state configured according to the modulespecification, any actuator including at least an electrical, hydraulic,or pneumatic actuator, a solenoid, an op-amp, analog control elements(springs, filters, integrators, adders, dividers, gain elements), and/ordigital control elements. In the illustrated embodiment, controller 140is connected to oxygen sensor(s) 142, engine sensor(s) 144, fuelsensor(s) 146, and exhaust sensor(s) 148 as discussed further below.

The listing herein of specific implementation elements is not limiting,and any implementation element for any controller described herein thatwould be understood by one of skill in the art is contemplated herein.The controllers herein, once the operations are described, are capableof numerous hardware and/or computer based implementations, many of thespecific implementations of which involve mechanical steps for one ofskill in the art having the benefit of the disclosures herein and theunderstanding of the operations of the controllers provided by thepresent disclosure.

One of skill in the art, having the benefit of the disclosures herein,will recognize that the controllers, control systems and control methodsdisclosed herein are structured to perform operations that improvevarious technologies and provide improvements in various technologicalfields. Without limitation, example and non-limiting technologyimprovements include improvements in combustion performance of internalcombustion engines, improvements in emissions performance,aftertreatment system performance, engine torque generation and torquecontrol, engine fuel economy performance, improved durability of exhaustsystem components for internal combustion engines, and engine noise andvibration control. Without limitation, example and non-limitingtechnological fields that are improved include the technological fieldsof internal combustion engines and related apparatuses and systems aswell as vehicles including the same.

Example parameters related to the operation of the engine 102 determinedby sensors 142, 144, 146, 148 which can be real or virtual, include anyengine operating parameters that affect or can be correlated to thecombustion conditions of cylinders 108, such as the fresh air (intake)mass flow, charge mass flow, and/or EGR mass flow. In some embodiments,one or more of oxygen sensors 142, 148 are oxygen sensors such asuniversal exhaust gas oxygen (UEGO) or heated exhaust gas oxygen (HEGO)sensors, and engine sensor(s) 144 measure a crank angle position ofengine 102. Further example and non-limiting parameters related to theoperation of the engine 102 measured by engine sensor(s) 144 can includean induction gas temperature at the intake passage 114, an induction gastemperature at the intake manifold 112, an induction gas pressure at theintake manifold 112, an exhaust gas temperature at the exhaust manifold116, an exhaust gas pressure at the exhaust manifold 116, an exhaust gastemperature at the inlet and/or outlet of the exhaust passage 120, anexhaust gas pressure at the inlet and/or outlet of the exhaust passage120, an exhaust gas temperature at the inlet and/or outlet of the EGRpassage 118, an exhaust gas pressure at the inlet and/or outlet of theEGR passage 118, a lift, duration and/or timing of an intake valveand/or an exhaust valve of cylinders 108, a speed of compressor 126, ageometry, position and/or speed of the turbine 128, a composition ofinduction gas and/or EGR gas, an engine speed value, an engine load,engine torque, engine power output value, an engine knock value, and/orcombinations thereof. Fuel sensor(s) 146 can measure or provide a signalindicative of a rate of fuel injection, a type of fuel injected, and/ora composition of the fuel. Additionally or alternatively, an exampleparameter includes a rate of change or other transformation of anydescribed parameter. The listed parameters are exemplary andnon-limiting.

Certain operations described herein include operations to interpret ordetermine one or more parameters. Interpreting or determining, asutilized herein, includes receiving values by any method known in theart, including at least receiving values from a datalink or networkcommunication, receiving an electronic signal (e.g. a voltage,frequency, current, or PWM signal) indicative of the value, receiving asoftware parameter indicative of the value, reading the value from amemory location on a non-transient computer readable storage medium,receiving the value as a run-time parameter by any means known in theart, and/or by receiving a value by which the interpreted or determinedparameter can be calculated, and/or by referencing a default value thatis interpreted or determined to be the parameter value.

In certain embodiments, the controller 140 provides a control command,and one or more components of the system 100 are responsive to thecontrol command. The control command, in certain embodiments, includesone or more messages, and/or includes one or more parameters structuredto provide instructions to the various engine components responsive tothe control command. An engine component responding to the controlcommand may follow the command, receive the command as a competinginstruction with other command inputs, utilize the command as a targetvalue or a limit value, and/or progress in a controlled manner toward aresponse consistent with the engine control command.

Certain systems are described in the following, and include examples ofcontroller operations in various contexts of the present disclosure. Inone embodiment shown in FIG. 2, a control scheme 200 includes engine 102and an oxygen sensor such as oxygen sensor 142 or 148. Sensor 142, 148provides a sensed lambda output 202 that is provided to a lambda controlmodule 204 of controller 140, which determines a lambda control feedbackcorrection input 208 based on the sensed lambda output and providesinput 208 to the fuel control module 206. As shown in graphs 300 and 301of FIG. 3A, if the AFRs of cylinders 108 are balanced, then thefrequencies of control feedback correction input 208 and sensed lambdaoutput 202 should be the same, although amplitude and phase may bedifferent. As shown graphs 302 and 303 of FIG. 3B, if the cylinder AFRsare imbalanced, then only the sensed lambda includes high frequencycomponents in the sensed signal since high frequency components of thecontrol feedback correction input 208 are filtered out in the controllerdue to controller bandwidth.

In one embodiment, an AFR imbalance diagnostic in controller 140 employsthe lambda control feedback correction input 208 and sensed lambdaoutput 202 to determine a cylinder AFR imbalance. In one embodiment, anAFR imbalance diagnostic procedure performed by controller 140 includesdetermining if monitoring conditions for an AFR imbalance diagnostic aremet; determining the fundamental frequency of the lambda controlfeedback correction input 208 (controller 140 feedback) using a timedomain method; determining the fundamental frequency of output lambda202 (sensed voltage) using a time domain method; determining amonitoring parameter in response to the fundamental frequencies;comparing the monitoring parameter to a pre-defined threshold; if themonitoring parameter is greater than the pre-defined threshold,determine and/or output of an AFR imbalance fault or if not then declarean AFR imbalance pass; and repeat these steps.

In one embodiment, the enable conditions include, for example, theengine speed being greater than a threshold, the mass air flow to theengine being greater than a threshold, the oxygen sensor heater beingON, intake manifold pressure being less than a threshold, and ditheringbeing ACTIVE. Other embodiments contemplate additional or alternativeenablement conditions. These enablement conditions may also be employedfor the other embodiment diagnostic procedures discussed herein. Instill other embodiments, a time duration for enablement conditions beingmet must be greater than a threshold time duration. A samplingrequirement may also be established.

In one embodiment, the monitoring parameter is a mean value of theabsolute difference of the input/output lambda frequencies. For example,as shown in graphs 400 and 401 of FIG. 4A, the feedback correction input208 may be determined by the inverse of the period of the falling edgeof the frequency, and the sensed lambda output 202 may be determined bythe inverse of the period of center crossing from high to low of theoxygen sensor output. The time domain method is used to estimate thefundamental frequency using mean crossing detection.

Another embodiment AFR imbalance diagnostic procedure performed bycontroller 140 decomposes the sensor measurements from an oxygen typesensor 142 into different harmonic components as shown in FIG. 4B and asfollows:y(t)=d(t)+x(t)+e(t)  measurement:d(t)=A _(dc)(t)+A _(d)(t)sin(∫₀ ^(t)2πf _(d)(τ)dτ+φ _(d))  ditheringterm:

-   -   DC+low frequency harmonic contents (˜3 Hz)    -   time-varying frequency and amplitude

${{imbalance}\mspace{14mu}{term}\text{:}\mspace{14mu}{x(t)}} = {\sum\limits_{k = 1}^{n_{cyl}}{{A_{k}(t)}{\sin\left( {{\int_{0}^{t}{2\pi\;{f_{cyc}(\tau)}d\;\tau}} + \varphi_{k}} \right)}}}$

-   -   engine cycle frequency    -   time-varying frequency and amplitude

uncertain term: e(t)

-   -   unknown, may include harmonics and/or white noise

The objective of this embodiment is to extract the features of x(t) fromy(t) to at least estimate the amplitude or power spectral density (PSD)or, at best, estimate the exact signal {circumflex over (x)}(t). In oneembodiment, a discrete fourier transform (DFT) is used fornon-parametric spectral analysis for a non-stationary signal, such asshown in a graph 500 of FIG. 5. A sliding DFT (SDFT) determines the PSDat the frequency of interest only, while a DFT determines PSD of allfrequencies up to a half sampling frequency. The use of a recursiveimplementation of DFT (SDFT) to determine AFR imbalance can be asfollows:

nominal form:

${X\left( {n,k} \right)} = {\left\{ {{X\left( {{n - 1},k} \right)} + {x(n)} - {x\left( {n - N} \right)}} \right\}\exp\frac{j\; 2\pi\; k}{N}}$

-   -   input—sample at time n: x(n)    -   output—temporal PSD at time n and frequency k: X(n,k)    -   transfer function:

${H\left( {z,k} \right)} = \frac{\left( {1 - z^{- N}} \right)\exp\frac{j\; 2\pi\; k}{N}}{1 - {\exp\frac{j\; 2\pi\; k}{N}z^{- 1}}}$

-   -   -   marginally stable→might be unstable w.r.t. actual data            (numerical reason, ex: round)

    -   stable form with damping factor r:

${X\left( {n,k} \right)} = {\left\{ {{r{X\left( {{n - 1},k} \right)}} + {x(n)} - {r^{N}{x\left( {{n - N},k} \right)}}} \right\}\exp\frac{j2\pi k}{N}}$

-   -   transfer function:

${H\left( {z,k} \right)} = \frac{\left( {1 - {r^{N}z^{- N}}} \right)\exp\frac{j\; 2\pi\; k}{N}}{1 - {r\;\exp\frac{j\; 2\pi\; k}{N}z^{- 1}}}$

In a further embodiment, a group energy (GE) concept is employed withSDFT to determine a monitoring parameter, such as a mean value of groupenergy around the cycle frequency, where the mean is a function of(GE(n, k(n))). GE can be defined:

Parseval's theorem:

${\sum\limits_{n = 0}^{N - 1}\;{{x(n)}}^{2}} = {\frac{1}{N}{\sum\limits_{k = 0}^{N - 1}\;{{X(k)}}^{2}}}$

Definition:

${G{E(k)}} = \sqrt{\sum\limits_{p = {- m}}^{m}{{X\left( {k + p} \right)}}^{2}}$

-   -   k: frequency index    -   a notch filter (i.e. band-pass filter) in frequency domain

GE with SDFT is:

Definition:

${G{E\left( {n,{k(n)}} \right)}} = \sqrt{\sum\limits_{p = {- m}}^{m}{{X\left( {n,{{k(n)} + p}} \right)}}^{2}}$

-   -   k(n): time-varying cycle frequency index at time n    -   a TV notch filter (i.e. TV band-pass filter) in time-frequency        domain

In one embodiment, a procedure performed by controller 140 to diagnosean AFR imbalance condition includes determining if monitoring conditionsare met to enable detection of an AFR imbalance condition; filling abuffer with inputs from the signals from oxygen sensor 142 to use in theSDFT analysis; calculating the SDFT around the cycle frequency;calculating a group energy from the SDFT; determining the monitoringparameter in response to a mean value of the group energy around thecycle frequency during the monitoring period; comparing the monitoringparameter to a pre-defined threshold; if the monitoring parameter isgreater than the threshold, declare a fault, otherwise declare a pass;and repeat these steps.

Another embodiment AFR imbalance diagnostic procedure performs aparametric spectral analysis of the sensor measurements from an oxygentype sensor 142 in the time domain and in the frequency domain as shownin blocks 600 and 601 of FIG. 6. The parametric spectral analysis ismodel based for a non-stationary signal with good separation between thenormal and fault (AFR imbalance) operating modes. In one embodiment, themodel is a time-varying auto-regressive (TV AR) model. The AR model formis as follows:y(n)=Σ_(k=1) ^(p) a _(k)(n)y(n−k)+e(n)

-   measured signal at time n: y(n)=d(n)+x(n)+e(n)∈-   model order predetermined: p-   time-varying model parameters at time n: [a_(k)(n)]_(k=1, . . . ,p)-   model error: e(n)∈

The state space model form is:ā(n+1)=ā(n)+ w (n),y(n)=C(n)ā(n)+e(n)

-   state vector: ā(n)=[a₁(n) a₂(n) . . . a_(p)(n)]^(T)∈    ^(p×1)-   stochastic uncertainty: w(n)∈    ^(p×1)-   output matrix: C(n)=[y(n−1) y(n−2) y(n−2) . . . y(n−p)]∈    ^(1×p)

The model parameter estimation ā(n) may employ a standard Kalman filter(KF) with computation load O(p²) (cf. RLS with a forgetting factorO(p²)) to estimate dithering and imbalance signals. In anotherembodiment, a time varying notch filter is employed to estimatedithering and imbalance signals. The tuning parameters include theconstant variance of stochastic uncertainty (V_(w)) and model error(V_(e)). The time-varying power spectral density (TV PSD) of the TV ARmodel is:

${Y\left( {n,{\omega_{cyc}(n)}} \right)} = {\frac{\sigma_{e}(n)}{1 - {\sum\limits_{k = 1}^{p}{{a_{k}(n)}{\exp\left( {{- k}\;{\omega_{cyc}(n)}j} \right)}}}}}$time-varying standard aviation (TV STD) of mod error: σ_(s)(n)The disclosed procedure determines an AFR imbalance based on TV STD forTV PSD with constant STD for KF to provide robustness.

A tuning guide for V_(w) and V_(e) is as follows:

V_(e) < V_(w) V_(e) > V_(w) adaptability high low model performance goodbad spectral analysis accuracy bad good

The recursive STD of model error σ_(e)(n) is:

mean standard deviation recursive update${\overset{\_}{e}(n)} = {{\overset{\_}{e}\left( {n - 1} \right)} + \frac{{e(n)} - {\overset{\_}{e}\left( {n - 1} \right)}}{n}}$${\sigma_{e}^{2}(n)} = {{\sigma_{e}^{2}\left( {n - 1} \right)} + {{\overset{\_}{e}}^{2}\left( {n - 1} \right)} - {{\overset{\_}{e}}^{2}(n)} + \frac{{e^{2}(n)} - {\sigma_{e}^{2}\left( {n - 1} \right)} - {{\overset{\_}{e}}^{2}\left( {n - 1} \right)}}{n}}$The monitoring metric is the mean value of the TV PSD:mean(∥Y(n,ω _(cyc)(n)∥)

In one embodiment, a procedure performed by controller 140 to diagnosean AFR imbalance condition includes determining if monitoring conditionsare met to enable detection of an AFR imbalance condition; initializingand executing a Kalman Filter or an RLS estimator to estimatetime-varying AR model coefficients from the sensor signals; determiningPSD at cycle efficiency from identified model coefficients; determininga monitoring parameter from the mean value of the time-varying PSD atcycle frequency over a monitoring period; compare the monitoringparameter to a pre-defined threshold if the monitoring parameter isgreater than the threshold, declare a fault, otherwise declare a pass;and repeat these steps.

In certain embodiments, controller 140 can be configured to provide afueling command to one or more of the cylinders 108 in response to thecylinder AFR imbalance condition that reduces the AFR imbalance. As aresult, the fueling amount provided to identified cylinder(s)contributing to the AFR imbalance varies from the fueling amountprovided to the other cylinders 108 to correct for flow imbalances inthe charge flow and injector variations, for example.

Having a balanced AFR between cylinders can improve engine performanceand emission controls. Having different AFR between cylinders (cylinderimbalance) can result in higher emission, higher fuel consumption,knock, misfire, and many other practical issues. The systems, apparatusand methods disclosed herein diagnose or estimate the existence ofcylinder-to-cylinder AFR variation or imbalance, and then issue a faultin response to the AFR imbalance being present.

Various aspects of the present disclosure are contemplated. According toone aspect, a method for diagnosing an AFR imbalance condition duringoperation of an internal combustion engine includes: determining one ormore enable conditions for diagnosing the AFR imbalance condition aremet; in response to one or more enable conditions being met, determininga first fundamental frequency of a lambda control feedback correctioninput using a time domain method; determining a second fundamentalfrequency of a sensed output lambda in an exhaust flow from one or morecylinders of the internal combustion engine using a time domain method;determining a monitoring parameter associated with the AFR imbalancecondition in response to the first fundamental frequency and the secondfundamental frequency; comparing the monitoring parameter to apre-defined threshold; and if the monitoring parameter is greater thanthe pre-defined threshold, determine and/or output of an AFR imbalancefault or otherwise declare an AFR imbalance pass.

In one embodiment, the one or more enable conditions include: a speed ofthe internal combustion engine being greater than a speed threshold; amass air flow to the internal combustion engine being greater than amass air flow threshold, an oxygen sensor heater being ON, intakemanifold pressure being less than a threshold, and dithering beingACTIVE. In another embodiment, the monitoring parameter is a mean valueof the absolute difference between the first and second fundamentalfrequencies. In yet another embodiment, the first fundamental frequencyis an inverse of a falling edge of the lambda control feedbackcorrection input and the second fundamental frequency is an inverse of aperiod of center crossing from high to low of the sensed output lambda.In still another embodiment, the method includes controlling a fuelingamount to the internal combustion engine to reduce the AFR imbalance inresponse to the AFR imbalance fault.

According to another aspect, a method for diagnosing an AFR imbalancecondition during operation of an internal combustion engine includes:determining one or more monitoring conditions are met to enabledetection of an AFR imbalance condition; in response to one or moreenable conditions being met, filling a buffer with a plurality of inputsto use in a sliding discrete fourier transform (SDFT) analysis, theplurality of inputs including a sensed output lambda in an exhaust flowfrom one or more cylinders of the internal combustion engine;determining SDFTs at various frequency components including cyclefrequency and its harmonics; determining a group energy from thedetermined SDFTs; determining a monitoring parameter in response to amean value of the group energy around the cycle frequency during themonitoring period; and comparing the monitoring parameter to apre-defined threshold and if the monitoring parameter is greater thanthe threshold, declare a fault relating to the AFR imbalance orotherwise declare an AFR imbalance pass.

In one embodiment, the one or more enable conditions include: a speed ofthe internal combustion engine being greater than a speed threshold; amass air flow to the internal combustion engine being greater than amass air flow threshold, an oxygen sensor heater being ON, intakemanifold pressure being less than a threshold, and dithering beingACTIVE. In another embodiment, the method includes controlling a fuelingamount to the internal combustion engine to reduce the AFR imbalance inresponse to the fault.

According to another aspect, a method for diagnosing an AFR imbalancecondition during operation of an internal combustion engine includesdetermining if one or more monitoring conditions are met to enabledetection of an AFR imbalance condition; initializing and executing aKalman Filter or an RLS estimator to estimate time-varyingauto-regressive (TV AR) model coefficients; determining a power spectraldensity (PSD) at cycle frequency from identified (TV AR) modelcoefficients; determining a monitoring parameter from a mean value ofthe time-varying PSD at cycle frequency over a monitoring period; andcomparing the monitoring parameter to a pre-defined threshold and inresponse to the monitoring parameter being greater than the thresholddeclare a fault.

In one embodiment, the one or more enable conditions include: a speed ofthe internal combustion engine being greater than a speed threshold; amass air flow to the internal combustion engine being greater than amass air flow threshold, an oxygen sensor heater being ON, intakemanifold pressure being less than a threshold, and dithering beingACTIVE. In another embodiment, the method includes controlling a fuelingamount to the internal combustion engine to reduce the AFR imbalance inresponse to the fault.

In another aspect, a method for diagnosing an AFR imbalance conditionduring operation of an internal combustion engine includes: determiningif one or more monitoring conditions are met to enable detection of anAFR imbalance condition; determining a monitoring parameter based on asensed lambda output from an oxygen sensor measuring an exhaust oxygenof the internal combustion engine; and comparing the monitoringparameter to a pre-defined threshold and in response to the monitoringparameter being greater than the threshold declare a fault.

In one embodiment, the method includes controlling a fueling amount tothe internal combustion engine to reduce the AFR imbalance in responseto the fault.

While the invention has been illustrated and described in detail in thedrawings and foregoing description, the same is to be considered asillustrative and not restrictive in character, it being understood thatonly certain exemplary embodiments have been shown and described. Thoseskilled in the art will appreciate that many modifications are possiblein the example embodiments without materially departing from thisinvention. Accordingly, all such modifications are intended to beincluded within the scope of this disclosure as defined in the followingclaims.

In reading the claims, it is intended that when words such as “a,” “an,”“at least one,” or “at least one portion” are used there is no intentionto limit the claim to only one item unless specifically stated to thecontrary in the claim. When the language “at least a portion” and/or “aportion” is used the item can include a portion and/or the entire itemunless specifically stated to the contrary.

What is claimed is:
 1. A method for diagnosing an air-fuel ratio (AFR)imbalance condition during operation of an internal combustion engine,comprising: determining one or more monitoring conditions are met toenable detection of an AFR imbalance condition; in response to one ormore enable conditions being met, filling a buffer with a plurality ofinputs to use in a sliding discrete fourier transform (SDFT) analysis,the plurality of inputs including a sensed output lambda in an exhaustflow from one or more cylinders of the internal combustion engine;determining SDFTs at various frequency components including cyclefrequency and its harmonics; determining a group energy from thedetermined SDFTs; determining a monitoring parameter in response to amean value of the group energy around the cycle frequency during themonitoring period; and comparing the monitoring parameter to apre-defined threshold and if the monitoring parameter is greater thanthe threshold, declare a fault relating to the AFR imbalance orotherwise declare an AFR imbalance pass.
 2. The method of claim 1,wherein the one or more enable conditions include at least one of: aspeed of the internal combustion engine being greater than a speedthreshold; a mass air flow to the internal combustion engine beinggreater than a mass air flow threshold, an oxygen sensor heater beingON, intake manifold pressure being less than a threshold, and ditheringbeing ACTIVE.
 3. The method of claim 1, further comprising controlling afueling amount to the internal combustion engine to reduce the AFRimbalance in response to the fault.
 4. The method of claim 1, whereinthe one or more enable conditions include a speed of the internalcombustion engine being greater than a speed threshold.
 5. The method ofclaim 1, wherein the one or more enable conditions include a mass airflow to the internal combustion engine being greater than a mass airflow threshold.
 6. The method of claim 1, wherein the one or more enableconditions include an oxygen sensor heater being ON.
 7. The method ofclaim 1, wherein the one or more enable conditions include an intakemanifold pressure being less than a threshold.
 8. The method of claim 1,wherein the one or more enable conditions include dithering beingACTIVE.
 9. The method of claim 1, wherein the one or more enableconditions include all of a speed of the internal combustion enginebeing greater than a speed threshold; a mass air flow to the internalcombustion engine being greater than a mass air flow threshold, anoxygen sensor heater being ON, intake manifold pressure being less thana threshold, and dithering being ACTIVE.
 10. An electronic controlapparatus for diagnosing an air-fuel ratio (AFR) imbalance conditionduring operation of an internal combustion engine, comprising: anelectronic controller configured to: determine one or more monitoringconditions are met to enable detection of an AFR imbalance condition ofthe internal combustion engine; in response to one or more enableconditions being met, fill a buffer with a plurality of inputs to use ina sliding discrete fourier transform (SDFT) analysis, the plurality ofinputs including a sensed output lambda in an exhaust flow from one ormore cylinders of the internal combustion engine; determine SDFTs atvarious frequency components including cycle frequency and itsharmonics; determine a group energy from the determined SDFTs; determinea monitoring parameter in response to a mean value of the group energyaround the cycle frequency during the monitoring period; and compare themonitoring parameter to a pre-defined threshold and in response to themonitoring parameter being greater than the pre-defined threshold,declare a fault relating to the AFR imbalance or otherwise declare anAFR imbalance pass.
 11. The electronic control apparatus of claim 10,wherein the one or more enable conditions include a speed of theinternal combustion engine being greater than a speed threshold; a massair flow to the internal combustion engine being greater than a mass airflow threshold, an oxygen sensor heater being ON, intake manifoldpressure being less than a threshold, and dithering being ACTIVE. 12.The electronic control apparatus of claim 10, wherein the electroniccontroller is configured to control a fueling amount to the internalcombustion engine to reduce the AFR imbalance in response to the fault.13. The electronic control apparatus of claim 10, wherein the one ormore enable conditions include a speed of the internal combustion enginebeing greater than a speed threshold.
 14. The electronic controlapparatus of claim 10, wherein the one or more enable conditions includea mass air flow to the internal combustion engine being greater than amass air flow threshold.
 15. The electronic control apparatus of claim10, wherein the one or more enable conditions include an oxygen sensorheater being ON.
 16. The electronic control apparatus of claim 10,wherein the one or more enable conditions include an intake manifoldpressure being less than a threshold.
 17. The electronic controlapparatus of claim 10, wherein the one or more enable conditions includedithering being ACTIVE.